 ```Fixed Income Investments
TI BA II Plus&reg; Calculator
Functions
Agenda

Mean, variance, and standard deviation

Covariance and correlation

NPV and IRR

Time value of money

Interest rate conversions
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1
Clearing the Memory


Typical reason for wrong answers is failing to clear
memory.
All “spreadsheet” functions (e.g., Data, CF, etc.) are
cleared via 2nd CE/C.


Important: you must be inside the function to clear it!
Time value of money is cleared via 2nd FV (CLR TVM).
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Functions
Income Calculator
Investments
Mean, Variance, and
Standard Deviation
2
Measures of Central Tendency:
Population and Sample Means
Population and sample means have different symbols
but are both arithmetic means.
N
population mean: μ =
X
i
i=1
N
n
X
i
sample mean: X =
i=1
n
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Population Variance and
Standard Deviation
Variance is the average
Standard deviation is
of the squared deviations the square root of
from the mean.
variance.
N
σ
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2
=
 X
i
i= 1
N
 μ
2
σ =
σ
2
6
3
Sample Variance (s2) and Sample Standard
Deviation (s)
 X
n
s
2
=
i
 X
i=1

 X
n
2
s =
n 1
i
 X
i= 1

2
n 1
Key difference between calculation of σ2 and s2 is that the
sum of the squared deviations for s2 is divided by n – 1
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Mean, Variance, and Standard Deviation
Over the last 3 years, Cerny Plc’s stock returns have been
as follows:
Year
% Return
1
6
2
8
3
4
May be entered as
decimals or whole
numbers
Calculate the mean, variance, and standard deviation.
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8
4
Mean, Variance, and Standard Deviation



To do this, we use 2nd 7 (Data) to input the values (skip Y)
and then 2nd 8 (Stat) to calculate the statistics.
When you press 2nd 8, the calculator must display 1-V. (If
not, press 2nd Enter to toggle through to it.)
Important: once in the Data spreadsheet, always start
by clearing the memory (2nd CE/C).
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Mean and Variance With Probabilities
Cerny Plc’s expected stock return for next year is as
follows:
May be entered as
decimals or whole
numbers
% Return
Probability
6
0.3
8
0.2
4
0.5
Must be entered as
whole numbers
Calculate the mean, variance, and standard deviation with
probabilities.
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5
Mean and Variance With Probabilities



To do this, we use 2nd 7 (Data) to input the values and then
2nd 8 (Stat) to calculate the statistics.
Returns are always input as X and probabilities as Y.
Important: the probabilities must be percentages, not
decimals (e.g., input 20% as 20, not 0.20).
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Functions
Income Calculator
Investments
Covariance and Correlation
6
Sample Covariance
Year
1
2
3
Stock 1
+0.05
–0.02
+0.12
Stock 2
+0.07
–0.04
+0.18
Example: Calculate the covariance between the return on
the two stocks indicated above:
n
c o v 1,2 
  R t,1  R 1 R t,2  R 2  
t 1
n 1
May be entered as
decimals or whole
numbers
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Covariance and Correlation




Press 2nd 7 as usual and input the data for X and Y.
Press 2nd 8 and select LIN by pressing 2nd Enter as
needed.
cov
r
=
therefore, cov = r &times; s x &times; s y
Remember:
sx sy
Press “Down Arrow” to find r, sx, and sy, and calculate their
product.
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7
Functions
Income Calculator
Investments
NPV and IRR
Net Present Value (NPV)
The sum of the present values of a series of cash flows
N P V  C F0 
C F1
C F2
C Fn


...

(1  k )1
(1  k ) 2
(1  k ) n
Discount rate (k) is cost of capital to the firm doing that project;
NPV is very useful for assessing feasibility of projects.
NPV ≥ 0  ACCEPT PROJECT!
NPV &lt; 0  REJECT PROJECT!
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8
Internal Rate of Return (IRR)
 IRR is the discount rate that equates the PV of a series
of cash flows to their cost.
 The IRR is the discount rate that makes the NPV = 0.
N P V  0  C F0 
C F1
C F2
C Fn



...
(1  IR R )1
(1  IR R ) 2
(1  IR R ) n
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Net Present Value (NPV)
Example: using a 10% discount rate
T0
T1
T2
T3
T4
\$25
\$100
\$75
\$50
i = 10%
–\$175
NPV is the change in wealth in present value terms
from a series of cash flows.
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9
NPV and IRR



This is done through “CF,” “NPV,” and “IRR” buttons on second
row.
Press CF and input the data.
Cash-flow frequency (F01…etc) should be left as 1 unless same
cash flow occurs multiple times.

Press NPV, input rate as %, press Down Arrow, and press CPT.

To calculate IRR, press IRR then CPT.
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Functions
Income Calculator
Investments
Time Value of Money
10
Time Value of Money
TVM are the 5 keys on 3rd row
N = number of periods
I/Y = periodic interest rate
PMT
PMT
+
I
1+
1+ I
Y
Y


2
+ .. ... +

PMT
1+ I

N
Y
+

FV
1+ I

N
Y
= PV
PV = present value
PMT = periodic payment
FV = future value
Calculator in END mode for PV (see Intro to BA video for all basic settings)
Important: clear memory through 2nd FV
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TVM – Bond Pricing
60
60
60
1000
+
+ ..... +
+
= PV
2
6
6
1 .0 7  1 .0 7 
1 .0 7  1 .0 7 
Example: Security required return is 7%; makes 6 annual payments of
\$60 each beginning one year from today and a payment of \$1,000 after 6
years.
Calculator in END mode; clear the memory before you start via 2nd FV!
6 N, 7 I/Y, 60 PMT, 1,000 FV, CPT PV
Displays –952.3346
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11
TVM – Yield to Maturity
Example: A \$100 7% semi-annual bond maturing in 5 years is trading at
98. What is its yield to maturity ?
Clear the memory!
5 &times; 2 = N, (98) PV, 7 / 2 = PMT, 100 FV, CPT I/Y &times; 2
Displays 7.49%
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TVM – Mortgage Example
Example: A homebuyer borrows \$300,000 on a fully-amortizable, 25-year
mortgage at an annual rate of 4%. What is the monthly mortgage
payment?
Clear the memory!
25 &times; 12 = N, 300,000 PV, 4% / 12 = I/Y, CPT PMT
Displays \$1,583.51
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12
TVM – Spot Rate from Discount Factor
Example: The 1.5 year discount factor is 0.975. What is the 1.5 year spot
rate?
Instead of using the formula, we could use TVM.
Clear the memory!
1
z(t) = 2
d(t)
1
2t
–1
1.5 &times; 2 = N, (0.975) PV, 1 FV, CPT I/Y &times; 2 =
Displays 1.695%
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Functions
Income Calculator
Investments
Interest Rate Conversions
13
Interest Rate Conversions
A bank pays 0.5% interest per month.
What is the nominal annual rate?
nominal = periodic rate &times; # of periods = 0.5% &times; 12 = 6%
What is the effective annual rate?
n
 nom 
 0.06 
effective =  1+
– 1=  1+




n 
12 
12
– 1= 6.168%
To avoid the above formula, use the rate conversion function (next slide).
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